A new, simple test has been developed to detect a particular type of cancer. The test must be evaluated before it is put into use. A medical researcher selects a random sample of 1000adults and finds (by other means) that 3%have this type of cancer. Each of the1000adults is given the test, and it is found that the test indicates cancer in 96%of those who have it and in 1%of those who do not. Based on these results, what is the probability of a randomly chosen person having cancer given that the test indicates cancer? Of a person having cancer given that the test does not indicate cancer?

A new, simple test has been developed to detect a particular type of cancer. The test must be evaluated before it is put into use. A medical researcher selects a random sample of 1000adults and finds (by other means) that 3%have this type of cancer. Each of the1000adults is given the test, and it is found that the test indicates cancer in 96%of those who have it and in 1%of those who do not. Based on these results, what is the probability of a randomly chosen person having cancer given that the test indicates cancer? Of a person having cancer given that the test does not indicate cancer?

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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A researchers is interested in the amount of sleep an individual receives after consuming a sleeping aid (Melatonin, Valerian root, and Placebo). The researcher randomly selects individuals into either group. However, some individuals drop out of the study which results in unequal sample sizes. Melatonin: n=6, M=14, T=84, SS=60 Valerian: n=10, M=13, T=130, SS=90 Placebo: n=4, M=9, T=36, SS=37 N=20, G=250, x2=3377 State the conclusion of these findings.
A homeopathic drug company developed a new drug designed to prevent colds. The company claims there is no difference between the effectiveness for men and women. To test the claim they chose a simple random sample of 100 women and 150 men who participated in the trial.At the end of the study, 56% of the women caught a cold, and 40% of the men caught a cold. Based on these findings we are testing to see if there is a difference in the effectiveness for women and men.a) Define the parameter(s) of interest.b) State the Hypotheses.c) Find the value of the relevant sample statistic using correct notation:_________________________ Based on the randomization distribution below, what is the p-value ____________________
Researchers studying starfish collected two independent random samples of 40 starfish. One sample came from an ocean area in the north, and the other sample came from an ocean area in the south. Of the 40 starfish from the north, 6 were found to be over 8 inches in length. Of the 40 starfish from the south, 11 were found to be over 8 inches in length. Which of the following is the test statistic for the appropriate test to investigate whether there is a difference in proportion of starfish over 8 inches in length in the two ocean areas (north minus south) ? 6−11640+1140√ A 6−110.1540+0.27540√ B 0.15−0.275(0.15)(0.275)(140+140)√ C 0.15−0.275(0.2125)(0.7875)(140+140)√ D 0.15−0.275(0.2125)(0.7875)140+140√
Travelers who have no intention of showing up often fail to cancel their hotel reservations in a timely manner. These travelers are known, in the parlance of the hospitality trade, as “no-shows”. To protect against no-shows and late cancellations, hotels invariably overbook rooms. A recent study examined the problems of over-booking rooms in the hotel industry. The following data, extracted from the study represent the daily numbers of late cancellations and no-shows for a random sample of 10 days at a hotel: 18, 16, 16, 16, 14, 18, 16, 18, 14, 19. c) Count the number of measurements that actually fall within the interval(x¯−2s, x¯+2s){ and express the interval count as a percentage of total number of measurements
Suppose that 73.2% of all adults with type 2 diabetes also suffer from hypertension. After developing a new drug to treat type 2 diabetes, a team of researchers at a pharmaceutical company wanted to know if their drug had any impact on the incidence of hypertension for diabetics who took their drug. The researchers selected a random sample of 1000 participants who had been taking their drug as part of a recent large-scale clinical trial and found that 718 suffered from hypertension. The researchers want to use a one‑sample ?z‑test for a population proportion to see if the proportion of type 2 diabetics who have hypertension while taking their new drug, ?p, is different from the proportion of all type 2 diabetics who have hypertension. They decide to use a significance level of ?=0.01α=0.01. Determine the value of the ?z‑test statistic. Give your answer precise to two decimal places. Determine the ?-valueP-value for this test. Give your answer precise to three decimal places.
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an automobile engineer claims that 1in 10 automobile accidents are due to driver fatigue . if a random sample of 5 accidents observed , then the probabilty that 3 accidentsare due to drive fatigue is
A study used 1259 patients who had suffered a stroke. The study randomly assigned each subject to an aspirin treatment or a placebo treatment. During a 3-year follow-up period, in Sample 1, 634 people received placebo treatments and 25 people died from heart attack. In sample 2, 625 people received aspirin treatment and 18 died from heart attack. Let pl denote the population proportion of death from heart attack for those with no treatment and p2 denote the population proportion of death from heart attack for those with aspirin treatment. (c) Which of SEO and SE1 is used for calculating a confidence interval for comparing two population proportions? Which is used for calculating the test statistic in a hypothesis test? (d) Construct the 95% confidence interval for pi – p2. Interpret.
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An industrial psychologist feels that a big factor in job turnover among assembly line workers is the individual employee’s self-esteem. She thinks that workers who change jobs often (Population A) have, on the average, lower self-esteem, as measured by a standardized test, than workers whodo not (Population B). To determine whether she can support her belief with statistical analysis, she draws a simple random sample of employees from each population and gives each a test measuring self-esteem. The results are as follows: Group A 60 45 42 62 68 54 52 55 44 41 Group B 70 72 74 74 76 91 71 78 76 78 83 50 52 66 65 53 52 The psychologist believes that the relevant population scores are normally distributed, with equal, although unknown, variances. At the 0.1 level of significance, what should she conclude
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A random sample of n1 = 157 people ages 16 to 19 were taken from the island of Oahu, Hawaii, and 12 were found to be high school dropouts. Another random sample of n2 = 129 people ages 16 to 19 were taken from Sweetwater County, Wyoming, and 6 were found to be high school dropouts. Do these data indicate that the population proportion of high school dropouts on Oahu is different (either way) from that of Sweetwater County? Use a 1% level of significance. (a) What is the level of significance? What is the value of the sample test statistic? (Test the difference p1 − p2. Do not use rounded values. Round your final answer to two decimal places.) (c) Find (or estimate) the P-value. (Round your answer to four decimal places.)